WASHINGTON - The head of the U.S. Senate Judiciary Committee says the woman accusing Supreme Court nominee Brett Kavanaugh of sexually assaulting her has until Friday morning to indicate she plans to testify before the panel in a hearing Monday.

California psychology professor Christine Blasey Ford has accused Kavanaugh of sexually assaulting her 36 years ago when both were in high school, an alleged attack that left Ford fearful for her life. Kavanaugh has denied the claims.

WATCH: Fate of Supreme Court Nominee Rests With a Divided Senate

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"As you know, I have reopened the hearing on Judge Kavanaugh's nomination in light of Dr. Ford's allegations," Chairman Chuck Grassley said in a letter Wednesday. "That hearing will begin again on Monday, September 25, at 10 a.m. I have invited Dr. Ford to testify regarding her allegations against Judge Kavanaugh. And in recognition of how difficult it can be to discuss allegations of this kind in public, I have also offered her the choice of testifying in either a public or closed session of the hearing."

Ford has not indicated whether she will attend the hearing. Her lawyers have called for an FBI probe of her allegations before she testifies.

"The rush to a hearing is unnecessary, and contrary to the committee discovering the truth," Lisa Banks, one of Ford's lawyers, said in a statement to CNN on Wednesday.

Banks said Ford and her family have received threats, which has caused them to leave their home.

"She continues to believe that a full, nonpartisan investigation of this matter is needed, and she is willing to cooperate with the committee," Banks said. "However, the committee's stated plan to move forward with a hearing that has only two witnesses is not a fair or good faith investigation; there are multiple witnesses whose names have appeared publicly and should be included in any proceeding."

The Senate Judiciary Committee is considering Kavanaugh's nomination for a lifetime seat on the country's highest court.

Republicans hold a slim majority in the Senate. The Judiciary Committee had been expected to vote on Kavanaugh Thursday, but that was pushed back after Ford went public with her accusation in a Washington Post article.

Many Republicans have called for the confirmation process to go forward, accusing Democrats of trying to stall. Democrats have said there is no need to rush and that the allegations should be fully considered.

#KremlinAnnex protesters place a sign referring to Christine Blasey Ford, the woman who accused Supreme Court nominee Judge Brett Kavanaugh of a 1982 sexual assault, and spell out the word 'AMORAL' on the 66th consecutive day of their demonstration outside the White House, Washington, Sept. 19, 2018.

Democrats seek FBI inquiry

That continued Wednesday with Democratic Senator Kamala Harris saying Republican opposition to an FBI probe "doesn't make sense."

"Members of the U.S. Senate should exercise due diligence, not rush toward a vote for a lifetime appointment. The people we represent didn't send us here to shirk our duty," she said.

Republican Senator Orrin Hatch wrote in the Washington Examiner that both Kavanaugh and Ford should directly address the allegations before the committee, but that Democrats have mishandled the process.

"No matter the outcome, Democrats should be held responsible for circumventing the very process that protects people like Ford. Their decision to reveal this allegation at the most politically damaging moment reeks of opportunism," Hatch said.

Democratic Senator Dianne Feinstein, to whom Ford wrote a letter in July outlining her allegations, has defended the timing of how the information became public, saying it was only appropriate for Ford to make that decision.

President Donald Trump expressed support for his nominee Wednesday, saying that "it's very hard for me to imagine" that Kavanaugh sexually assaulted Ford.

Trump said he hopes Ford testifies at Monday's hearing.

"I really want to see her, to see what she has to say," Trump said of Ford, now 51. He said it "would be unfortunate" if she does not appear.

Meanwhile, Anita Hill, the law professor at the center of lurid 1991 confirmation hearings involving Clarence Thomas as a U.S. Supreme Court justice, supported Ford's call for an FBI investigation of her claims.

Hill told ABC's Good Morning America show: "The American public really is expecting something more. They want to know that the Senate takes this seriously."

Hill, now a law professor at Brandeis University, said Republican leaders are in an unnecessary rush to confirm Kavanaugh.

"Either they don't take this seriously," she said, "or ... they just want to get it over. I'm not sure which is in play. Maybe they're not concerned, or maybe they don't know how to handle this kind of situation."

The specter of Hill's allegations 27 years ago that Thomas often sexually harassed her when they both worked for a federal government agency hangs heavy over the current Kavanaugh confirmation proceedings.

Hill's accusations were largely dismissed then by the all-male Senate committee, but many American women sympathized with her claims against Thomas, saying they resonated with their own experiences in the workplace. Thomas was confirmed on a narrow Senate vote and remains a conservative stalwart on the court to this day.

Republican lawmakers are trying to win Senate confirmation for Kavanaugh ahead of the start of the court's new term, Oct. 1, or if not by then, ahead of the Nov. 6 nationwide congressional elections, to show Republican voters they have made good on campaign promises to place conservative judges like Kavanaugh on the Supreme Court.